The Abaque Rhabdologique of Claude Perrault

The Parisian doctor of medicine Claude Perrault (biography) was a remarkable person—a typical encyclopedical scientist from the end of European Reneisanse. Graduating as a doctor of medicine, in his long life he was interested and achieved remarkable results in the fields of architecture, anatomy, physics, mechanics, zoology, physiology, etc.

Eleven years after his death, in 1700, in Paris was published his small book—Recueil de plusieurs machines, de nouvelle invention. In its 22 pages of text and several pages of sketches are described nine inventions of Perrault. Between them are two machines for escalating and moving of burdens, a pendulum-controlled water clock, a pulley system to rotate the mirror of a reflecting telescope, and what is of a particular interest for us—a very interesting calculating device, called Abaque Rhabdologique.

In the 1699's year issue of the french journal Le Journal des sçavans (printed in 1701) was also published a description of the Abaque Rhabdologique (pages 55-59).

The device was designed probably between 1666 and 1675, but it is unknown whether a working copy of the device has been made by Perrault. In present day exists only several replicas (see the photo bellow).

A replica of the Perrault's calculating device

The Abaque Rhabdologique is a small metal plate (30 cm x 12 cm x 0,7 cm) with thickness of a finger (see the sketch below) and weight 1.15 kg.

The sketch of the Abaque Rhabdologique

Over the plate are mounted seven small rules (marked with letters a, b, c, d, e, f and g on the sketch), which can be moved upwards and downwards. The rules are graduated to 26 parts by deep cuts, and the edge of the pin, which actually moves the rules, can be push in these cuts. Between the cuts are drawn ascending and descending rows of digits, with four empty divisions between zeroes. The rule a represents the units column, the rule b—the decimal column, and so on to the rule g, which represents the millions. The rules are separated by thin plates, which have perforations in the bottom.

Near the bottom of the each rule (with the exception of the rule for units), to the right side, there is a rule with 11 notches (marked with L), and distance between notches is equal to the distance between digits, marked on the rules. From the other side of the rule with notches by means of springs are attached the hooks M. Due to the separating thin plates, the hook will be hidden in the body of the rule till the moment, when the hook will become symmetrical toward the opening in the plate. In this moment, the spring will push out the hook, which will pass the opening and will clutch to the notch of the lower rule and will move it one division downwards, making a carry to the next column.

On the front lid of the device ABCD are placed two long horizontal windows EF and GH. When the rulers are moving up or down, in these windows are seen the digits on the plates, and at every moment the sum of the digits of a particular ruler in upper and lower windows is always equal to 10. The window GH is used during adding operations, while the window EF is used during subtraction.

Between the windows are made 7 narrow vertical channels I-K, which are divided to 10 and marked with digits.

In the lower part of the lid is inscribed a multiplication table.

For entering a digit, in the particular cut of a ruler, which can be seen in the vertical channel, must be put a stylus, and then the ruler must be moved, until the stylus touched to the bottom edge of the channel. After this action, the number, which has been entered, will be shown simultaneously in the both windows.

If to an entered number, for example 7, must be add 6, we have to perform the same action. During the moving of the ruler a to the bottom of the device, the hook M will enter into cohesion with the cogs of the ruler b and will move it one division downwards. As a result of this in the decimal column will appear 1. In order to get the proper digit in the units column (which in this example must be 3), we have (without pulling the stylus out of the cut) to move the ruler upwards, until the stylus touched the bottom edge of the channel.

During the performing of a subtraction, the actions of the operator are analogous, but the result must be read not in the lower, but in the upper window. If the minuend contains one or several zeroes, the result of the operation must be corrected.

The simple and ingenious idea of the device of Claude Perrault was step aside from the common development of mechanical calculating devices, which are based on the gear-wheels. This idea will be applied after 2 centuries in the several cheap, simple and reliable calculating devices, such as the multi-column adding machine, designed in 1891 by Peter J. Landin of Minneapolis (US Patent 482312) (see the computer of Landin), which will be later produced in several countries in great quantities and many varieties, e. g. popular Comptator in Germany.

The Comptator adder from 1922, manufactured by Hans Sabielny, Dresden, Germany (Courtesy of Mr. John Wolf)